Review of International Economics, 21(5), 945–965, 2013
DOI:10.1111/roie.12081
Shouldn’t Physical Capital Also Matter for
Multinational Enterprise Activity?
Jeffrey H. Bergstrand and Peter Egger*
Abstract
The foreign direct investment (FDI) literature has generally failed to find strong systematic evidence of
“vertical” motivations in bilateral aggregate FDI and foreign affiliate sales (FAS) data, despite recent evidence of vertical FDI in firm-level data. Moreover, a Bayesian analysis of the empirical determinants of
FDI (and FAS) flows reveals that the parent country’s physical capital per worker has a strong positive
effect on FDI alongside typical gravity-equation variables; however, this variable is ignored in the
knowledge-capital (KC) model and most empirical work. We address these two puzzles by introducing relative factor endowment differences into the three-factor, three-country knowledge and physical capital
extension of the 2 × 2 × 2 KC model. Using a numerical version of our model, we show that horizontal and
vertical multinational enterprises’ (MNEs’) headquarters surface in different parts of the Edgeworth box
relating the parent country’s skilled labor share relative to its physical capital share (of the parent’s and
host’s endowments). The key economic insight is that horizontal MNE headquarters will be relatively more
abundant than vertical MNE headquarters in countries that are abundant in physical capital relative to
skilled labor, because of the multi-plant (single-plant) structure of horizontal (vertical) MNEs—assuming
plants (headquarters) use physical capital (skilled labor) relatively intensively in their setups. The theoretical relationships suggest augmenting empirical FAS gravity equations with (polynomials of) the parent’s
skilled labor share alongside the parent’s physical capital share to explain in aggregate bilateral data the
coexistence of horizontal and vertical FAS. The theoretical and empirical results shed light on the positive
effect of parent’s physical capital share on FAS flows, but also suggest that MNE headquarters may be
prominent in parent countries with relatively high and low skilled labor shares—once physical capital is
accounted for—a result not suggested by the two-factor KC model.
It seems clear that vertical motivations are not prevalent in the general FDI
patterns. (Bruce Blonigen, 2005)
1. Introduction
This paper addresses the issue of finding evidence of vertical multinational enterprise
(MNE) activity alongside horizontal MNE activity in aggregate bilateral data by
examining the seemingly “schizophrenic treatment” of physical capital in modern
analyses of foreign direct investment (FDI) and foreign affiliate sales (FAS). On the
one hand, the modern general equilibrium theory of MNE activity focuses upon the
role of intangible assets of firms—such as knowledge capital—for explaining MNEs’
existence, cf. Markusen (2002). Using the knowledge capital model, most empirical
analyses have focused upon the roles of relative economic sizes to explain “horizontal” MNE activity and relative skilled-to-unskilled labor ratios to explain “vertical”
* Bergstrand: Department of Finance, Mendoza College of Business and Kellogg Institute for International
Studies, University of Notre Dame and CESifo, Notre Dame, IN 46556, USA. Email: [email protected].
Egger: Department of Economics, ETH University, CESifo, and Ifo Institute, Weinbergstrasse 35, 8092
Zurich, Switzerland. The authors are grateful for very useful comments from the editor, an anonymous
referee, and participants at presentations at the University of Oxford, London School of Economics and
Political Science, Drexel University, European Trade Study Group annual conference, and Southern Economics Association annual conference.
© 2013 John Wiley & Sons Ltd
946
Jeffrey H. Bergstrand and Peter Egger
MNE activity, cf. Carr et al. (2001, 2003), Blonigen et al. (2003), Markusen and Maskus
(2001, 2002), Braconier et al. (2005), and Davies (2008). Motivated by a two-factor
model with only skilled and unskilled labor, physical capital plays no role theoretically
or empirically in these analyses.
On the other hand, Blonigen and Piger (2011) found evidence that bilateral aggregate FDI outflows are strongly and positively influenced by parent countries’ physical
capital per worker. Moreover, the extension of the international economics literature
to recognize “heterogenous productivities” among national, exporting, and multinational enterprises reveals that MNEs tend to be very physical-capital intensive (as
well as skilled labor intensive) firms and MNEs tend to be headquartered in relatively
physical-capital abundant (as well as skilled-labor abundant) countries, cf. Bernard
et al. (2005), Helpman et al. (2004), and Helpman (2006). Even one of the measures of
FDI in the US Bureau of Economic Analysis (BEA) data uses the share of a MNE’s
real investment in physical plant and equipment in a foreign affiliate. This schizophrenic treatment of physical capital in the MNE literature and the apparent absence
of “vertical motivations” for FDI in the bilateral aggregate data suggests
re-considering a role for physical capital.
In reality, of course, both relative physical capital to unskilled labor (K/U) and
skilled labor to unskilled labor (S/U) ratios are likely to influence aggregate bilateral
FDI/FAS flows in general equilibrium, alongside economic size and similarity as well
as investment costs. This paper addresses physical capital’s role theoretically and
empirically, and offers two potential contributions. First, we introduce differences in
relative physical capital endowments—alongside differences in relative skilled and
unskilled labor endowments—into the three-factor, three-country, two-good “Knowledge and Physical Capital” model of Bergstrand and Egger (2007) and provide some
testable hypotheses for predicted vertical and horizontal FAS that are different than
those suggested by the workhorse 2 × 2 × 2 “Knowledge Capital” (KC) model.
Bergstrand and Egger (2007) presented a three-country, three-factor, two-good extension of Markusen’s two-country, two-factor, two-good KC model, but assumed identical relative factor endowments to focus only on the roles of gross domestic product
(GDP) size and similarity for explaining the coexistence of horizontal bilateral FAS/
FDI flows and intra-industry trade flows for countries with identical absolute and relative factor endowments and for motivating a theoretical rationale for estimating
“gravity equations” of bilateral FAS and FDI flows alongside bilateral trade flows.
Vertical MNEs played no role in Bergstrand and Egger (2007). We find here that
general equilibrium relationships between relative skilled-to-unskilled labor ratios
and bilateral FAS are sensitive to relative endowments of physical capital. A key theoretical economic insight is that horizontal MNE headquarters will be relatively more
abundant than vertical MNE headquarters in countries that are abundant in physical
capital relative to skilled labor, because of the multi-plant (single-plant) structure of
horizontal (vertical) MNEs—assuming plants (headquarters) use physical capital
(skilled labor) relatively intensively in their setups. An implication of this is that physical capital rich economies will tend to have high levels of bilateral horizontal FAS
when skilled labor is scarce relative to physical capital and such economies will tend
to have high levels of bilateral vertical FAS when skilled labor is abundant relative to
physical capital (for given levels of unskilled labor). This suggests that the relationship
between a parent country’s skilled labor share (of two countries’ joint skilled labor
endowment) and the FAS of the parent country may be a fourth-order polynomial.1
Second, empirical explanations for determinants of bilateral international trade
flows have long used the “gravity equation,” the workhorse of international trade.
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
947
Moreover, the gravity equation is also the workhorse for empirical analysis of determinants of bilateral FAS and FDI flows.2 Using a Bayesian moving average (BMA)
analysis, Blonigen and Piger (2011) found inclusion probabilities of 100% for standard
gravity variables such as parent and host countries’ GDPs and the bilateral distance
between two countries. Moreover, they also found an inclusion probability for the parent’s capital stock per worker of 94%, but an inclusion probability of only 54% for the
parent’s education level. Our theoretical analysis suggests a rationale for the inclusion
of parent’s physical-capital share (of parent and host countries’ physical capital).
Moreover, our theoretical analysis suggests a rationale for including fourth-order
polynomials of the parent’s skilled labor share and of the parent’s physical capital
share in an augmented gravity equation. We find that the inclusion in a FAS gravity
equation of fourth-order polynomials of the parent country’s shares of (two countries
i and j) skilled labor and physical capital helps to explain the patterns of aggregate
bilateral FAS. Three empirical findings are notable. First, the parent’s skilled labor
share has the expected fourth-order polynomial relationship with bilateral FAS. In
fact, the empirically predicted bilateral FAS flows reveal two “peaks” in the empirical
Edgeworth-box space, one where horizontal MNE activity should be maximized and
one where vertical MNE activity should be maximized—consistent with the corresponding theoretical Edgeworth-box predictions. Second, the parent’s physical capital
share also has a significant effect on bilateral FAS, and the fourth-order polynomial
empirical relationship corresponds also with the model’s theoretical predictions.
Third, the parent’s unskilled labor share has the expected negative, monotonic
relationship with FAS. In the context of our model, our empirical results provide evidence for vertical motivations for FAS in the bilateral aggregate data, alongside horizontal motivations.3 In fact, we find evidence suggesting—consistent with firm-level
categorizations in Alfaro and Charlton (2009) of horizontal and vertical MNEs—that
vertical MNE (VMNE) motivations are as important as horizontal MNE (HMNE)
motivations.
The remainder of the paper is as follows. In section 2, we discuss the limitations of
the two-factor KC model for identifying vertical MNE activity separately from horizontal MNE activity in aggregate bilateral FAS data. In section 3, we summarize the
three-factor, three-country, two-good Knowledge and Physical Capital (KAPC) model
in Bergstrand and Egger (2007), allowing now asymmetric relative factor endowments. In section 4, we use the numerical version of our model to postulate theoretical
hypotheses about relationships between relative factor endowments and FAS. In
section 5, we examine empirically the determinants of bilateral aggregate FAS flows.
Section 6 concludes.
2. Limitations of the 2 × 2 × 2 Knowledge-Capital for Finding Vertical MNEs
We argue here that the evidence against the KC model in favor of just HMNEs
explaining bilateral aggregate FAS flows should actually come as no surprise if one
examines closely the theoretical predictions of the KC model—limited to a 2-factor,
2-country world. In the following, reference to the “KC model” necessarily implies a
2-factor, 2-country world. Figures 1a and 1b from Markusen (2002) and Figure 1c from
BNU help to illustrate this point, based upon the KC model. Figure 1a presents the
Edgeworth box (figure 7.1 from Markusen, 2002, p. 143) relating country i’s (j’s) share
of the two countries’ skilled labor stocks along the vertical axis, country i’s (j’s) share
of the two countries unskilled labor stocks (also called by Markusen the “composite
factor”) along the horizontal axis, and the equilibrium “regimes” of types of firms (see
© 2013 John Wiley & Sons Ltd
948
Jeffrey H. Bergstrand and Peter Egger
oj
World endowment of skilled labor
(a)
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
of
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
World endowment of the composite factor
Multinational firms only
Mixed regimes of national and multinational firms
Vertical firms
National firms only
(b)
Types of firms active in equilibrium: Regime (the number in the cell) = Idi + Ijd + Ivi + Ijv+ Iih + Ijh (I is for ìindicator ”)
102.000 102.000 102.000 102.000 102.000 102.000 102.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000
102.000 102.000 102.000 102.000 102.010 102.010 100.010 100.010 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.200 100.200
102.000 102.000 102.000 102.010 102.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.011 100.001 100.001 100.200 100.200
102.000 102.000 102.010 102.010 102.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.011 100.001 100.001 100.201 100.200
102.000 102.010 102.010 102.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.001 100.001 100.001 100.201 100.200
102.000 102.010 102.010 102.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.010 100.011 100.001 100.001 100.001
0.201
0.200
102.000 102.010 102.010 100.010 100.010 100.010 100.010 100.010 100.010
0.010
0.010
0.010
0.011 100.011 100.001 100.001 100.001
0.201
0.200
102.010 102.010 102.010 100.010 100.010 100.010
0.010
0.010
0.010
0. 010
0.011
0.011
0.011 100.011 100.001 100.001
0.201
0.201
0.201
2.010
2.010 102.010
0.010
0.010
0.010
0.010
0.010
0.011
0.011
0.011
0.011
0.011 100.001
0.001
0.001
0.201
0.201
0.201
2.010
2.010
2.010
0.010
0.010
0.010
0.010
0.011
0.011
0.011
0.011
0.011
0.001
0.001
0.001
0.001
0.201
0.201
0.201
2.010
2.010
2.010
0.010
0.010
10.010
0.011
0.011
0.011
0.011
0.011
0.001
0.001
0.001
0.001
0.001
10.201
0.201
0.201
2.010
2.010
2.010
10.010
10.010
10.011
0.011
0.011
0.011
0.001
0.001
0.001
0.001
10.001
10.001
10.001
10.201
10.201
10.201
2.000
2.010
10.010
10.010
10.010
10.011
0.011
0.001
0.001
0.001
10.001
10.001
10.001
10.001
10.001
10.001
10.201
10.201
10.200
2.000
12.010
10.010
10.010
10.010
10.011
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10. 001
10.201
10.201
10.201
10.200
12.000
12.010
10.010
10.010
10.010
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.201
10.201
10.201
10.200
12.000
12.010
10.010
10.010
10.011
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.201
10.201
10.201
10.200
10.200
12.000
12.000
10.010
10.010
10.011
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.001
10.201
10.201
10.200
10.200
10.200
12.000
12.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.001
10.001
10.201
10.201
10.200
10.200
10.200
10.200
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.200
10.200
10.200
10.200
10.200
10.200
10.200
Idi = 100 if type-di firms active, 0 otherwise
Ivi = 2.0 if type-vi firms active, 0 otherwise
Ihi = 0.01 if type-hi firms active, 0 otherwise
Idj = 10 if type-dj firms active, 0 otherwise
Ivj = 0.2 if type-vj firms active, 0 otherwise
Ihj = 0.001 if type-hj firms active, 0 otherwise
Peak of Vertical
FDI. (V)
(c)
Peak of Horizontal
FDI. (V)
Afiliate
sales
V
0i
Home country
origin (country i)
H
1
0
ui =
Host country
origin (country j)
0j
Ui
Ui + Uj
si =
Si
Si + Sj
10
Figure 1(a–c). Equilibrium Regimes of Types of Firms and Empirically Predicted
Foreign Affiliate Sales (a) Types of Firms Active in Equilibrium (b) Types of Firms
Active in Equilibrium: Regime ( the Number in the Cell ) = I id + I jd + I iv + I jv + I ih + I jh (I is
for “Indicator”) (c) Empirically Predicted Foreign Affiliate Sales
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
949
Figure 1a’s index). Depending upon relative skilled to unskilled labor ratios, HMNEs
(“Multinational firms only”), VMNEs (“Vertical firms”), NEs (“National firms only”),
or “Mixed regimes of national and multinational firms” may be found in equilibrium.
Cursory examination of this figure suggests two main propositions evaluated in the
KC literature. First, when two countries are identical in economic size and relative
factor endowments, both countries will have only HMNEs in equilibrium; there will
be no VMNEs (nor NEs or international trade, for that matter) in equilibrium.
Second, however, when country i is moderately relatively skill abundant (moving left
from the center cell, or towards the left vertical axis), HMNEs based in i will still exist
in equilibrium (because HMNEs’ headquarters setups use relatively more skilled
labor than NEs’ headquarters setups). Yet when country i becomes even more relatively skill abundant (further left), Figure 1a suggests that HMNEs cease to exist in i.
However, HMNEs are actually joined by VMNEs (because it becomes profitable for i
to “outsource” final goods production to j and ship output anywhere in the world), as
explained below.
Initial empirical estimation of the KC model to find both HMNEs and VMNEs in i
was virtually doomed to fail for the following reason. Figure 1b (actually table 7.2
from Markusen, 2002) reports the sum of different types of operations in existence in
equilibrium, which is the data underlying Figure 1a. Consider three results. First, at the
center cell (when the two countries are identical in absolute and relative factor
endowments), both countries have HMNEs headquartered in their own countries,
with plants in their home and foreign markets; no VMNEs or NEs are profitable
(0.011 = 0.010 + 0.001), consistent with Figure 1a. Second, moving leftward, country i
eventually becomes relatively smaller and more skilled-labor abundant, making
HMNEs based in i the only profitable firms (0.010), consistent with Figure 1a. Third,
continuing leftward, the three columns on the far left indicate that relatively skilledlabor abundant i will headquarter both HMNEs and VMNEs (2.010 = 2.0 + 0.010), as
explained in Markusen (2002, p. 145). That is, for the ratio of skilled-to-unskilled labor
in i shown in the far left column and middle row, FAS for home country i in host
country j is motivated by both horizontal and vertical activity! In fact, careful examination of the entire first (left-hand side) column of Figure 1b reveals that HMNEs
exist in equilibrium for moderate levels of skill abundance, but VMNEs exist also for
high, moderate, and low levels of skill abundance. The fundamental problem with
using the 2 × 2 × 2 KC model to distinguish VMNE from HMNE activity is this:
overlap of vertical and horizontal MNEs (cells in Figure 1b with values of either 2.01,
12.01, or 102.01) comprise 18% of the 190 cells in the upper-left quadrant of
Figure 1b, making it very difficult to distinguish VMNE from HMNE activity using
only relative factor endowments of skilled to unskilled labor.
Thus, Carr, Markusen, and Maskus (2001), or CMM (2001), econometric estimation
of the KC model to find both HMNEs and VMNEs was compromised from the start
because the Edgeworth surface described bilateral FAS motivated by both HMNEs
and VMNEs at the same skilled to unskilled labor ratio—even if the central regression “specification” was mapped directly from the theory as in Braconier et al. (2005),
or BNU, i.e. factor shares of the Edgeworth box.4 BNU made a useful contribution to
this literature by generating a regression specification that mapped “directly” from the
theoretical framework, taking into account properly the geometric considerations of
Edgeworth boxes. Motivated by this important analytical consideration alongside
employing a broader data set (in terms of country pair coverage) of FAS bilateral
flows, BNU argued that—when properly specified—VMNEs could be found in the
data, alongside HMNEs. Figure 1c (from Braconier et al., 2005) illustrates their
© 2013 John Wiley & Sons Ltd
950 Jeffrey H. Bergstrand and Peter Egger
“empirically predicted” FASij. However, while their empirically predicted FAS surface
is visually similar to the theoretically predicted FAS surface in Markusen (2002,
figure 10.1, p. 221), the problem still remains. Where BNU predict the “peak of vertical
FDIij” in Figure 1c—when i is economically smaller and skilled-labor abundant relative to j—the data cells in Figure 1b inform us that both vertical and horizontal MNEs
can be headquartered in i (note the cell entry 2.010 in the far left column in rows 9, 10,
11, and 12). Thus, BNU does not resolve the issue empirically because the problem lies
in finding—in Edgeworth-box space—relative factor endowment configurations
where VMNE headquarters can be clearly distinguished from HMNE headquarters.
3. Theoretical Framework: A Summary of the Knowledge and Physical
Capital Model
The model we use is a more general version of the three-country, three-factor, twogood KAPC model in Bergstrand and Egger (2007) by allowing differences in relative
skilled to unskilled labor (S/U) ratios and relative physical capital to unskilled labor
(K/U) ratios, consequently generating horizontal and vertical MNEs as well as
national exporting enterprises (NEs) in equilibrium. Bergstrand and Egger (2007) is
an extension of the 2 × 2 × 2 KC model in Markusen (2002) with national exporters
(NEs), horizontal MNEs (HMNEs), and vertical MNEs (VMNEs). However,
Bergstrand and Egger (2007) assumed identical relative factor endowments to focus
on the roles of economic size and similarity and provide a theoretical foundation for
gravity equations of trade, FAS, and FDI simultaneously; consequently, no VMNEs
surfaced in that paper, except in one sensitivity analysis. The demand side in the
model is analogous to that in the KC model.
The key difference between our KAPC model and Markusen’s KC model is that we
add a third factor, physical capital (K), the services of which can be used at home or
transferred abroad (via FDI) either as a “greenfield” investment or an acquisition
(and not necessarily a costless transfer). We assume that all three internationally
immobile primary factors are used in the production of the differentiated good:
unskilled labor (U), skilled labor (S), and private physical capital (K). Moreover, following evidence from Griliches (1969), Goldin and Katz (1998), and Slaughter (2000),
we assume that skilled labor and physical capital are complements in production,
which is also consistent with evidence in Bernard et al. (2005) that MNEs tend to be
relatively abundant in countries that are relatively abundant in both skilled labor and
physical capital. However, for the setups of headquarters and plants, we assume that
the services of only skilled labor are used to setup headquarters and the services of
only physical capital are used to setup plants. HMNEs headquartered in any country i,
for example, arise endogenously, and the services of home physical capital are “used
up” (owing to their “rival” nature) to setup a plant in the home country or abroad to
maximize firm profits (with an implied no-arbitrage incentive for rates of return on
physical capital; no profits are left “on the table”), but physical capital need not actually move internationally. In the presence of imperfect international (financial) capital
mobility, firms may choose to have financial claims to physical capital at home or—via
FDI—abroad. The key distinction from knowledge capital is that claims to physical
capital are rival, and FDI—owing to foreign government restrictions—may not move
costlessly between countries. The second distinction of our model from the KC model
is to introduce a “third country,” Rest-of-World (ROW). The presence of the third
country helps explain the observed complementarity of bilateral FAS and trade flows
with respect to a country pair’s economic size and similarity and that bilateral FDI
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
951
and FAS tend empirically to be as well explained by a gravity equation as bilateral
trade flows are. Since the structure and calibration of the model is described explicitly
in Bergstrand and Egger (2007), to conserve space we present the model in Appendix
A and a description of the calibration of the model in Appendix B of this paper (both
available online at www.nd.edu/~jbergstr).
4. Theoretical Hypotheses
The numerical version of our general equilibrium model can be used to generate (at
least) three “testable propositions” relating pairs of countries’ relative factor endowments to aggregate bilateral FAS activity. We focus first on predicting theoretically the
numbers of HMNEs based in home country i with plants in i, j, and/or ROW, the
numbers of VMNEs based in home country i with plants in j or ROW, and the aggregate bilateral FAS of parent country i in host country j—contingent upon different
configurations of relative factor endowments. We use these predictions to suggest
three testable hypotheses about the relationship between a country pair ij’s relative
factor endowments and the FAS of headquarters country i with a foreign affiliate in
country j.
Owing to the presence of three factors, three countries, and highly nonlinear relationships, there are potentially an enormous number of relationships to explain. To
make the testable hypotheses tractable in a world with three factors, three countries,
and two goods, we use the “workhorse” tool of international trade—the Edgeworth
box—for studying relationships between relative factor endowments and FAS, as used
in Markusen (2002) and BNU. However, all the papers just noted assumed two-factor
worlds; we have a three-factor world.
In a three-factor world, Edgeworth boxes actually are slices from an Edgeworth
“cube,” showing the relationship between a flow and two countries’ shares of two
factors—for any given shares of the two countries of the third factor (and for any
given level of ROW’s endowments). To focus initially on the relationships between
physical capital, skilled labor, unskilled labor, and horizontal and vertical MNEs, we
consider first the Edgeworth box relationship between country i’s share of countries
i’s and j’s physical capital stocks (ki) for a given physical capital stock in ROW,
country i’s share of i’s and j’s skilled labor stocks (si) for a given skilled labor stock in
ROW, and the numbers of HMNEs and VMNEs headquartered in i—at the mean of
ui, which is i’s share of i’s and j’s unskilled labor endowments (for a given unskilled
labor endowment in ROW). Henceforth, FASij denotes the theoretically predicted
bilateral FAS of parent/home country i in host country j; later in the empirical work,
FASij (without italics) denotes the empirically predicted bilateral FAS of MNEs with
headquarters in i and plants in j.
Since we are examining the relationships among ki, si, and determinants of FASij,
our relationships are conditional upon the level of ui (a third factor) as well as the
economic size of ROW (a third country). Because we will pursue a regression analysis
later, it will be useful to show slices of the Edgeworth cube at the empirical mean of
the implicit third factor, say ui. The reason is that—in a regression of bilateral FAS on
numerous variables—the interpretation of, say, the coefficient estimate for ki would be
holding constant si and ui at their “means”; thus, the theoretical predictions relating,
say, the numbers of HMNEs in i with plants in j with ki and si are being made at the
mean of ui. However, it will be convenient now to note that the empirical means for ki,
si, and ui all range between 0.53 and 0.56. Hence, for convenience, the mean of each
factor share is effectively 0.50.5
© 2013 John Wiley & Sons Ltd
952
Jeffrey H. Bergstrand and Peter Egger
Theoretically Predicted VMNEs of i with Plants in j
Theoretically Predicted HMNEs of i with Plants in j
100
100
50
50
0.95
0
0.95
0
0.725
0.725
0.225
0.50
0.225
0.50
0.725
si
0.50
0.50
0.225
0.725
ki
0.95
0.225
0.95
si
(a) Mean of ui
ki
(b) Mean of ui
Theoretically Predicted FAS of i in j
100
50
0
0.95
0.725
0.225
0.50
0.50
0.725
si
0.225
0.95
ki
(c) Mean of ui
Figure 2(a–c). Theoretically Predicted Numbers of HMNEs, Numbers of VMNEs, and
Foreign Affiliate Sales (a) Mean of ui (b) Mean of ui (c) Mean of ui
Our first testable hypothesis (Hypothesis 1) builds on two theoretical results:
Result 1: The number of HMNEs based in i with plants in j will be maximized when i is
abundant in physical capital relative to skilled labor relative to j, owing to the multiplant structure of HMNEs and plant (headquarters) setups being physical capital
(skilled labor) intensive; and
Result 2: The number of VMNEs based in i with a plant in country j will be maximized
when i is abundant in skilled labor relative to physical capital relative to j, owing to
the single-plant structure of VMNEs alongside the assumed physical capital intensity
of plant setups relative to headquarters setups.
Figures 2a and b illustrate the relationships between ki, si, and the numbers of
HMNEs based in i with plants in j (and ROW) and VMNEs based in i with plants in
j, respectively, evaluated at the empirical mean of ui (effectively, 0.5). Consider
Figure 2a first. HMNEs are multi-plant structures, whose plant setups are physical
capital intensive (specifically, such setups are intensive in the internationally-mobile
“services” of physical capital via FDI). Consequently, HMNEs will be abundant in
country i if i is abundant in physical capital relative to skilled labor (and also to
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
953
unskilled labor), as shown in Figure 2a (i.e. ki > si). By contrast, VMNEs require only
one plant (located abroad) along with its headquarters (located at home). Since
headquarters setups use skilled labor services and plant setups use physical capital
services, VMNEs will be prominent in i when skilled labor and physical capital are
both abundant relative to j (and assuming ui = 0.5) and skilled labor is only slightly
more abundant in i than physical capital (as all MNE headquarters setups require
more skilled labor than NE setups). Figure 2b illustrates the theoretical relationships
between ki, si, and the number of VMNEs headquartered in i with a plant in j at the
mean of ui. Figure 2b suggests that VMNEs will be prominent in i when skilled labor
is slightly more abundant than physical capital, as a result of the single-plant, singleheadquarters structure of VMNEs. The key economic insight is that—assuming
plants (headquarters) are physical capital (skilled labor) services intensive in
setups—countries that are physical capital abundant (scarce) relative to skilled labor
should tend to headquarter HMNEs (VMNEs), for given ui and given endowments
in ROW.
Figures 2a and b together suggest that empirical FASij may in a regression be
fourth-order polynomial function of si, as illustrated in Figure 2c. Figure 2c provides
the model’s depiction of theoretical FASij. Consider first si. If we are interested in
the relationship between variation in si and FASij, then we must hold constant ki and
ui at their means (about 0.5). Figure 2c represents the relationships between si, ki,
and FASij—evaluated at the mean of ui (ui = 0.5). In Figure 2c, we see from varying
si from 0 to 1 at the mean of ki (ki = 0.5), and knowing that this Edgeworth “slice” is
at ui = 0.5, that there are three inflection points. This implies that FASij is a fourthorder polynomial function of si, as horizontal FASij is generated by HMNEs of
country i with plants in j and vertical FASij is generated by VMNEs of country i
with plants in j. Specifically, at ki = ui = 0.5, assume si = 0 initially. There will be
no HMNEs or VMNEs headquartered in i. As si increases from 0, the relative abundance of physical capital (since ki = 0.5) causes HMNEs in i to become profitable
first and the number of HMNEs increases (Figure 2a) and FASij rises above
0. However, as si continues to rise past 0.5, physical capital becomes scarce relative
to skilled labor (as ki = 0.5), reducing the profitability of HMNEs in i, but increasing the profitability of VMNEs in i since VMNEs have only one plant to setup
abroad, requiring less physical capital than an HMNE. This suggests testable
Hypothesis 1:
Hypothesis 1: Empirical FASij in a regression should be a fourth-order
polynomial function of si at the means of ki and ui (ki = ui = 0.5).
For robustness, we generated the theoretical k–s surfaces for the numbers of VMNEs
and HMNEs in i also for ui at the 30th and 70th percentiles. The shapes of the theoretical surfaces are qualitatively the same; figures omitted for brevity, but available on
request.6
We now consider the theoretical relationship between ki and FASij. If we are interested in the relationship between variation in ki and FASij, then we must hold constant
si and ui at their means (0.5). Figures 3a and b present the theoretical Edgeworth
boxes relating ki, ui, and the numbers of HMNEs and VMNEs headquartered in i with
affiliates in j, respectively, at si = 0.5. Figure 3a shows that HMNE headquarters will be
prominent in i when physical capital is abundant; this makes intuitive sense since
multi-plant HMNEs require physical capital for setups. However, at si = ui = 0.5, as ki
falls from 1, the number of HMNEs headquartered in i declines. But as shown in
Figure 3b, as ki falls closer to 0.5, skilled labor becomes abundant in i relative to physi© 2013 John Wiley & Sons Ltd
954
Jeffrey H. Bergstrand and Peter Egger
Theoretically Predicted VMNEs of i with Plants in j
Theoretically Predicted HMNEs of i with Plants in j
100
100
80
80
60
60
40
40
20
20
0
0.95
0.725
0.225
0.50
0.725
0.225
0.50
0.725
0.95
0
0.95
0.225
0.725
ki
ui
0.50
0.50
0.225
0.95
ui
(a) Mean of si
ki
(b) Mean of si
Theoretically Predicted FAS of i in j
100
80
60
40
20
0
0.95
0.725
0.225
0.50
0.50
0.225
0.725
0.95
ui
ki
(c) Mean of si
Figure 3(a–c). Theoretically Predicted Numbers of HMNEs, Numbers of VMNEs, and
Foreign Affiliate Sales (a) Mean of si (b) Mean of si (c) Mean of si
cal capital, making it profitable for VMNEs to surface in i. This suggests that the relationship between ki and FASij is also a fourth-order polynomial. This suggests testable
Hypothesis 2:
Hypothesis 2: Empirical FASij in a regression should be a fourth-order
polynomial function of ki at the means of si and ui (si = ui = 0.5).
For completeness, Figure 3c shows the relationships between ki, ui and FASij. Figure 3c
requires careful inspection; it is both quantitatively and qualitatively different from
Figure 3b at ui = 0.5. In Figure 3b, at ui = 0.5 when i is very physical capital abundant
(ki = 1.0), there are no VMNEs headquarted in i. However, Figure 3c shows that at
ui = 0.5 and ki = 1.0 there is positive FASij; this FASij is entirely horizontal FASij (see
Figure 3a). As ki decreases from ki = 1.0 along ui = 0.5, horizontal MNEs decline in
Figure 3c owing to the fall in physical capital abundance relative to skilled labor, but
vertical MNEs increase. However, as ki continues to decline toward 0, even VMNEs
headquarted in i become unprofitable. Thus, we expect empirical FASij to be a fourthorder polynomial function of ki at the means of si and ui (0.5).
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
955
In anticipation of our empirical results, we offer one note of clarification. Note that
the z-axes in all figures (measuring FASij) are indexed to 100. Hence, the more limited
effect of HMNEs FAS in Figure 3c relative to vertical FAS reflects the calibration of
the model. In the numerical simulations, at the peaks vertical MNE FAS activity is
larger than HMNE FAS activity. This is apparent also in Figure 2c. It should be noted
that our hypotheses are only qualitative predictions, not quantitative ones; we do not
necessarily expect vertical FASij to exceed horizontal FASij. Indeed, earlier empirical
evaluations suggest that, if anything, horizontal FAS activity should dominate vertical
FAS activity. Our goal here is to introduce physical capital in such a manner as to
suggest an empirical regression specification to better distinguish vertical FAS from
horizontal FAS. We leave it to the data to reveal the relative quantitative importance
of the two sources of FAS activity.
Finally, Figures 3a, 3b, and 3c all suggest Hypothesis 3, which is also potentially
testable:
Hypothesis 3: Empirical FASij should be a negative monotonic function of
u i.
The reason is that at ki = 0.5 and si = 0.5 an increase in ui is associated with an unambiguous decline in FASij. The economic rationale is straightforward. If country i’s
share of unskilled labor increases, i’s comparative advantage in production—of either
differentiated good X or homogeneous good Y—increases, and consequently it loses a
comparative advantage in hosting multinational headquarters, either horizontal or
vertical ones.
This expected relationship is confirmed for FASij in si–ui space; again, FASij is
decreasing in ui monotonically.7 For robustness Figures 4a–b depict the relationships
in si–ui space, which correspond to the axes in BNU. Figure 4a shows the theoretical
relationship between numbers of HMNEs with headquarters in i and plants in j (as
well as in i and ROW), si, and ui at ki = 0.5. Figure 4b shows the theoretical relationship between numbers of VMNEs with headquarters in i and plants in j, si, and ui at
ki = 0.5. As expected, when ui is low and si is low, more HMNEs are headquartered in
i. When ui is low and si is high, more VMNEs are headquartered in i.
Theoretically Predicted VMNEs of i with Plants in j
Theoretically Predicted HMNEs of i with plants in j
100
100
80
80
60
60
40
40
20
20
0.95
0
0.725
0.225
0.50
0.50
0.225
0.725
0.95
ui
(a) Mean of ki
0.95
0
0.725
0.225
0.50
0.50
0.725
si
0.225
0.95
si
ui
(b) Mean of ki
Figure 4(a,b). Theoretically Predicted Numbers of HMNEs and VMNEs (a) Mean of
ki (b) Mean of ki
© 2013 John Wiley & Sons Ltd
956
Jeffrey H. Bergstrand and Peter Egger
5. Empirical Framework and Results
Empirical Framework
The three-factor, three-country, two-good theoretical framework and empirical
evidence in Bergstrand and Egger (2007) provides the starting point for a
central regression specification—that is, a gravity equation—to capture economic
size and similarity and bilateral trade and investment costs in determining bilateral
horizontal FAS and bilateral intra-industry trade, consistent with Blonigen and
Piger’s (2011) Bayesian Moving Average analysis that confirmed the empirical
importance of gravity-equation variables.8 However, Bergstrand and Egger
(2007) provided no conceptual guidance on the specification of relative factor
endowments.
BNU provided three important contributions to empirical investigation of the roles
of relative factor endowments for explaining FAS flows in the two-factor, two-country
KC model. One contribution was to extend empirical analysis from just US inward
and outward FAS flows to a broad sample of countries. We follow this suggestion
using bilateral FAS data from the United Nations Conference on Trade and Development (UNCTAD) country profiles for 1986–2000 among 36 countries listed in the
Data Appendix; unfortunately, a consistent bilateral FAS data set among a larger
number of countries is unavailable. Second, BNU measured relative factor endowments of skilled and unskilled labor using factor endowment share measures implied
directly by Edgeworth-box (geometric) considerations (i.e. si and ui). We follow this
suggestion as well, and detail in the next paragraph how we adapt it to our threefactor, three-country setting. Third, BNU summarized the empirically predicted FAS
values (based upon their final regression specification) using an Edgeworth box to
confirm visually the “goodness of fit,” alongside conventional R2 measures; we adopt
this later.
The second BNU methodological innovation just noted reminds us that a country’s
factor shares measure precisely the “location” of a pair of countries in an Edgeworth
box. First, we know from the 2 × 2 × 2 KC literature that a traditional two-dimensional
Edgeworth box can be used theoretically to reflect the relationship between si, ui, and
bilateral FAS of headquarters country i in affiliate country j (FASij). Hence, a regression equation trying to capture the theoretical surfaces relating vertical FAS and horizontal FAS to relative factor endowments implied by the Edgeworth box should
include si and ui explicitly. Moreover, in a three-factor setting, we are in an Edgeworth
“cube.” Hence, to evaluate a slice of the cube—say, for a given ki—the regression must
include ki to hold it constant (at its mean). For given absolute endowments, a regression specification for capturing the relationships between FASij, si, ui, and ki should
include—on the right-hand side—si, ui, and ki explicitly in some functional form suggested by theory.
Second, a critical assumption of an Edgeworth box is that absolute factor endowments are held constant. In the two-country case, this is accounted for by including the
two countries’ GDPs, as the gravity equation would suggest; in cross-section, as is well
established, the correlation between GDP and absolute factor endowments is very
high (so that inclusion of GDP for economic size is sufficient). However, the threecountry methodology of Bergstrand and Egger (2007) suggests that the GDPs of
countries i, j, and ROW need to be accounted for. In a large cross-section, ROW GDP
variation is virtually zero, and so need not be included. In a panel, changes in ROW
GDP are easily accounted for using time dummies.
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
957
Consequently, our regression specifications to explain bilateral FAS flows basically
“wed” the methodological contributions of Bergstrand and Egger (2007)—suggesting
a standard gravity equation to account for economic size (or absolute factor endowments), trade costs, and investment costs—and of BNU—suggesting the use of factor
shares si, ui, and ki to account for relative factor endowments. Typical gravity equation
specifications include several variables to capture bilateral trade and/or investment
costs. In this regard, we include standard time-invariant bilateral “cost” variables: the
log of bilateral distance, a dummy variable for common land border (1 if adjacent, and
0 otherwise), and a dummy variable for common official language (1 if the same, and 0
otherwise). Following Markusen (2002), we also include cross-sectional and timevarying logarithms of multilateral measures of country trade resistance and investment resistance indexes from CMM (2001): log(Tci), log(Tcj), and log(Invcj).
Unfortunately, data constraints preclude bilateral measures, which would be preferable. Third, in the specifications below, we include a time “dummy” for each year
(except one, becouse of the constant) to capture potentially time-varying ROW GDP;
however, for brevity we do not report the coefficient estimates for the intercept and
time dummies.9
For estimation, we use a Poisson quasi-maximum likelihood (PQML) approach,
which has become widely accepted. The reason for the PQML estimation method is
the following. First, because of the multiplicative relationship between levels of flows
and their economic determinants and owing to Jensen’s inequality, in the presence of
heteroskedasticity ordinary least squares (OLS) estimation of log-linearized equations may lead to biased coefficient estimates for right-hand side variables. The PQML
estimation method can address this concern, cf. Santos Silva and Tenreyro (2006).
Second, PQML can be applied with dependent variables that include zero and positively valued observations, such as FAS flows. PQML exploits variation from both
zero and non-zero observations, and our theoretical model predicts a large number of
zeros and our empirical FAS data set has a large number of zeros. Data sources are
listed in the Data Appendix.
Empirical Results
Regression results Table 1 reports various specifications for PQML regressions for
bilateral FAS flows. The first two columns in Table 1 provide, respectively, a list of the
right-hand side variables and their expected coefficient signs. The third through ninth
columns report coefficient estimates and z-statistics (in parentheses) for specifications
1–7 for explaining bilateral FAS.
Specification 1 provides the results of estimating a traditional gravity equation for
FASij, where right-hand side variables capture economic size (a proxy for absolute
factor endowments) and similarity and various factors that either impede or
enhance flows. Since GDPiGDPj = (GDPi + GDPj)2{[GDPi/(GDPi + GDPj)][GDPj/
(GDPi + GDPj)]}, we include separately log(GDPi + GDPj) and log(Similarityij)
where Similarityij = [GDPi/(GDPi + GDPj)][GDPj/(GDPi + GDPj)]. Economic size
and similarity have the expected positive and statistically significant relationships
with FASij.The two coefficient estimates suggest a clear “horizontal motivation” for
MNE activity, as in Bergstrand and Egger (2007).
We now discuss the other “traditional” gravity-equation variables included in specification 1. As often found, the log of bilateral distance has a negative and statistically
significant coefficient estimate and a conventional value throughout all the specifications (and so we will provide no further discussion of it). Of course, as in the KC
© 2013 John Wiley & Sons Ltd
958
Jeffrey H. Bergstrand and Peter Egger
Table 1. Bilateral FAS PQML Regressions
Variables
Expected
sign
log(GDPi +
GDPj)
log(Similarityij)
+
log(Distanceij)
—
Contiguity
?
Language
+
log(Invcj)
—
log(Tcj)
?
log(Tci)
—
si
+
si2
—
si3
+
si4
—
ki
+
ki2
—
ki3
+
ki4
—
ui
—
siki
?
siui
?
kiui
?
+
No. of Obs.
Pseudo R2
FAS
(1)
FAS
(2)
FAS
(3)
FAS
(4)
FAS
(5)
FAS
(6)
2.08*
2.07*
2.06*
2.19*
2.10*
2.33*
(20.21) (19.71) (19.69) (22.76) (20.03) (19.86)
0.13*
0.17*
0.16*
(2.36)
(2.72)
(2.46)
−0.70* −0.67* −0.67* −0.69* −0.66* −0.64*
(−15.41) (−15.41) (−14.27) (−14.88) (−15.30) (−14.94)
0.25*
0.27*
0.35*
0.36*
0.33*
0.27*
(2.61)
(2.84)
(3.11)
(3.08)
(2.97)
(2.40)
0.02
0.03
−0.00
−0.03
0.11
−0.07
(0.13)
(0.21) (−0.00) (−0.21)
(1.01) (−0.68)
−0.69* −0.69* −0.92* −0.84* −0.86* −0.85*
(−5.37) (−5.35) (−6.85) (−6.12) (−6.78) (−6.56)
−0.03
−0.14
−0.10
−0.11
−0.19* −0.14
(−0.31) (−1.57) (−1.20) (−1.35) (−2.24) (−1.62)
0.59*
0.74*
0.67*
0.54*
0.62*
0.56*
(6.23)
(7.42)
(6.46)
(5.40)
(6.71)
(6.15)
0.93*
0.32
0.02
26.63*
11.83*
(2.89)
(0.88)
(0.06)
(7.69)
(2.92)
−89.37* −55.65*
(−6.40) (−3.64)
113.89*
80.86*
(5.56)
(3.55)
−49.23* −36.61*
(−4.93) (−3.27)
2.39*
2.48*
3.06*
24.93*
(5.77)
(5.68)
(6.95)
(6.77)
−67.71*
(−4.86)
85.72*
(4.21)
−38.34*
(−3.96)
−0.97* −2.98* −2.87* −3.79* −3.73*
(−3.18) (−7.30) (−6.63) (−8.95) (−9.00)
1370
0.61
1370
0.61
1370
0.63
1370
0.63
1370
0.66
1370
0.67
FAS
(7)
2.36*
(18.35)
−0.61*
(−13.98)
0.25*
(2.23)
−0.06
(−0.55)
−0.79*
(−6.01)
−0.12
(−1.31)
0.57*
(6.42)
9.90*
(2.26)
−43.90*
(−2.87)
52.07*
(2.13)
−21.74
(−1.79)
29.25*
(7.36)
−93.09*
(−5.26)
118.67*
(5.04)
−54.87*
(−4.80)
−5.19*
(−6.07)
7.95
(1.22)
0.41
(0.08)
1.92
(0.43)
1370
0.67
Notes: * Denotes statistically significant at 5% in two-tailed z-test. Numbers in parentheses are z-statistics.
Coefficient estimates for the constant and time dummies are not presented for brevity.
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
959
literature, actual “distance” has no theoretical role, but is often interpreted as an
investment “friction” and typically included. We specify the expected sign on contiguity as ambiguous for FASij. The reason is that—if FAS has a horizontal motivation—
then FAS is a substitute for trade, and contiguity may have a negative effect (lower
trade costs cause more trade and less FAS). If contiguity reduces information costs,
then it may have a positive effect on FASij. In all the FAS specifications, Contiguity
has a positive and statistically significant effect. A common language is likely to
enhance information flows, and the expected effect is positive; in all the FAS specifications, the coefficient estimate is effectively zero and statistically insignificant. The log
of the investment cost index in j (log(Invcj)) is expected to have a negative effect on
FASij, representing a barrier to either vertical or horizontal investment in j. Throughout the FAS specifications, this variable has the expected negative sign and is statistically significant. Finally, we include two indexes of “trade costs,” one multilateral
trade-cost index for j (log(Tcj)) and one such index for i (log(Tci)). For log(Tcj), we
have no unambiguous sign expectation. The reason is that, if FAS has a horizontal
motivation, we would expect a positive coefficient, as FAS and trade are substitutes.
However, in reality, even HMNEs based in i with plants in j require some intermediate inputs from i, for which trade costs in j would impede FASij. It turns out that the
coefficient estimates for log(Tcj) tend to be effectively zero for most FAS specifications. Distance may be effectively capturing much of this variable’s cross-sectional
effect. Finally, the expected coefficient sign for log(Tci) is negative. If FASij has a vertical motivation, then we would expect goods to flow from j to i; trade costs in i would
diminish these flows. Hence, FASij may indirectly be reduced because of trade costs in
i; this creates a negative expected effect. However, the coefficient estimates for
log(Tci) are positive and statistically significant for all the FAS specifications, which is
unexpected. The overall pseudo-R2 value for specification 1 is 0.61, which is about the
same (0.58) as that for a similar gravity specification for FDI flows in Bergstrand and
Egger (2007).
We now turn to the focus of this paper, the effect of relative factor endowments on
FAS flows. Specification 2 enhances the FAS gravity equation, adding just si and ui to
the previous specification. The reason for reporting this specification—even though
our theoretical model suggests that si should be included as a fourth-order
polynomial—is to determine if we can find a similar (positive) effect as for the variables SKILLij (= si/ui) in BNU and SKDIFFij (measured as the difference in i’s and j’s
skilled labor stocks as shares of total labor force) in CMM (2001). We confirm this.10
Holding ui constant, si has a positive and statistically significant coefficient estimate
and—holding si constant—ui has a negative and statistically significant coefficient estimate; this suggests that there is some “vertical motivation” for FAS. Of course, this
specification is not motivated by our theoretical Edgeworth boxes and is subject to
the same potential specification concern as raised in Blonigen et al. (2003). However,
it is useful to ascertain that this simple specification “accords” with earlier results of
CMM and BNU motivated by the two-factor, two-country KC model. Finally, we note
that none of the other (gravity equation motivated) variables’ coefficient estimates
change materially, and so there remains evidence of “horizontal motivation” for FAS
as well.
In specification 3, we consider for the first time the role of physical capital endowments by adding ki to the previous specification. Interestingly, the only variable whose
coefficient estimate changes materially is i’s skilled labor share, si. This is interesting
because it suggests that measures of relative skilled labor endowments in previous
studies may have been effectively a proxy for relative physical capital endowments in
© 2013 John Wiley & Sons Ltd
960
Jeffrey H. Bergstrand and Peter Egger
explaining FAS. Only physical capital (ki) and unskilled labor (ui) factor endowment
shares—of the three relative endowment variables si, ki, and ui—are statistically
significant.
As noted earlier, the inclusion of variables si, ki, and ui maps relative factor shares
directly from the theory. However, also noted earlier, variation in any one variable—
such as si—for given values of ki and ui—necessarily (in an Edgeworth box) changes
relative economic sizes of i and j. Thus, one can argue that the change in any one
factor share (vertically or horizontally in the box) changes relative factor endowments
and economic size, so that the inclusion of log(Similarityij) is inappropriate. By these
considerations, we ran specification 4 which differs from previous specification 3 only
by the exclusion of log(Similarityij). The important outcome is that the exclusion of
log(Similarityij) does not create any significant omitted variables bias; none of the
other variables’ coefficient estimates changes materially. Consequently, in the remaining specifications we exclude log(Similarityij); however, for robustness all subsequent
specifications’ results are largely insensitive to its absence (and available on request).
Theoretical discussion in section 4, theoretical Figures 2a–c, and Hypothesis 1 imply
that—for given ki and ui—FASij should be a fourth-order polynomial function of si.
Specification 5 modifies the previous specification by including si, si2 , si3, and si4 . The
expected signs for these four variables’ coefficients in specification 5 for a fourthorder polynomial function to follow the shape suggested by theoretical Figure 2c at
the means of ki and ui (about 0.5) are listed in the second column of Table 1. Specification 5 shows that the coefficient estimates have the expected signs and all are statistically significant. Hence, in a comparison of specifications 4 and 5, si in specification 4
(without the fourth-order polynomial function) is economically and statistically insignificant, but using a fourth-order polynomial si has the expected theoretical relationship with FASij. Moreover, none of the other variables’ coefficient estimates changes
materially between specifications 4 and 5. Thus, Hypothesis 1 is confirmed empirically.
Section 4, theoretical Figures 3a–c, and Hypothesis 2 imply that—for given si and
ui—FASij should be a fourth-order polynomial function of ki. Specification 6 modifies
the previous specification by including ki, ki2 , ki3 , and ki4 . The expected signs for these
four variables’ coefficients in specification 6 for a fourth-order polynomial function to
follow the shape suggested by theoretical Figures 3a–c at the means of si and ui (0.5)
are listed in the second column of Table 1. Specification 6 shows that the coefficient
estimates follow a fourth-order polynomial function with coefficient estimate signs
corresponding precisely to the expected ones, and all coefficient estimates for these
four variables are statistically significant. Moreover, none of the other variables’ coefficient estimates changes materially between specification 5 and 6. Thus, Hypothesis 2
is confirmed empirically.
We note across all six FAS specifications that ui has the expected negative coefficient sign with statistical significance, confirming Hypothesis 3. This accords with the
intuition that FAS of MNEs based in i will be lower the relatively more unskilled
labor abundant i is, because unskilled labor raises its comparative advantage in production over forming MNE headquarters. Theoretical Figure 3c suggests a monotonic
negative relationship between FASij and ui. Indeed, FASij and ui are negatively correlated with a statistically significant coefficient estimate.
Even though the fourth-order polynomial functions for si and ki captured the theoretical relationships in Edgeworth-box space, as a robustness check we were curious
to see if specification 6’s results were sensitive to interaction terms, commonly used in
the KC literature. While many interaction terms are possible, we considered adding
only the interaction terms siki, siui, and kiui—that is, interactions among the key factor© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
961
share variables. Specification 7 reports the results of adding these interaction terms.
Interestingly, none of the coefficient estimates of the interaction terms was statistically
significantly different from zero. Moreover, their inclusion had no material impact on
the other coefficient estimates.
Empirically-predicted FAS flows In this section, we draw upon one of the innovations in BNU—which employed the empirically-predicted bilateral FAS flows using
its central regression equation—to examine the similarity of the Edgeworth boxes
using the theoretically predicted FASij and those using empirically predicted FASij.
Moreover, we must extend this approach in our three-factor setting to slices of an
Edgeworth “cube,” evaluating the Edgeworth slices at the empirical means of the
third factor.
Figure 5a provides the Edgeworth box relating empirically predicted FASij from
Specification 6 to ki and si at the empirical mean of ui (about 0.5) and provides empirical support for one of the main economic insights of this paper. This figure corresponds to theoretical Figure 2c (except for the relative quantitative importance of
HMNE vs VMNE activity). Predicted (empirical) FASij reaches a maximum when
Empirically Predicted FAS of i in j
Empirically Predicted FAS of i in j
100
80
60
40
20
0
100
50
0
0.95
0.725
0.225
0.50
0.95
0.225
0.50
0.50
0.725
si
0.725
0.50
0.725
0.225
0.95
ki
0.95
0.225
ki
ui
(a) Mean of ui
(b) Mean of si
Empirically Predicted FAS of i in j
100
80
60
40
20
0
0.95
0.225
0.725
0.50
0.50
0.725
0.95
ui
0.225
si
(c) Mean of ki
Figure 5(a–c). Empirically Predicted Foreign Affiliate Sales (a) Mean of ui (b) Mean of
si (c) Mean of ki
© 2013 John Wiley & Sons Ltd
962
Jeffrey H. Bergstrand and Peter Egger
either country i is abundant in skilled labor and physical capital (relative to unskilled
labor)—which favors VMNE activity (see theoretical Figure 2b)—or country i is
abundant in physical capital relative to skilled labor—which favors HMNE activity
(see theoretical Figure 2a). Figure 5a confirms empirically that both horizontal and
vertical FAS are important—but with HMNE activity more important empirically in
the aggregate bilateral data—and each type of FAS attains its maximum in the
Edgeworth box approximately where Figures 2a–c predict. Figure 5a is consistent with
Hypothesis 1; FASij is a fourth-order polynomial of si at the means of ki and ui.
Figure 5b confirms Hypotheses 2 and 3, but only upon careful examination.
Figure 5b provides the Edgeworth box relating empirically-predicted FASij to ki and ui
at the empirical mean of si and provides empirical support for two other main economic insights of this paper: FASij is a fourth-order polynomial function of ki and a
monotonic negative function of ui. The figure is the empirical analogue to theoretical
Figure 3c (except for the relative quantitative importance of HMNE vs VMNE activity). It is clear—when comparing Figure 5b with Figures 3a and b—that HMNE activity tends to dominate FAS activity in the bilateral aggregate data. However, vertical
MNE activity is not trivial; it is important to recall that the predicted (empirical) FASij
surface in Figure 5b is generated by the statistically significant fourth-order polynomials in ki and si. Indeed, careful examination of Figure 5b reveals that empirically predicted FASij’s are a fourth-order polynomial of ki for any given value of ui (and
recalling that si = 0.5). Moroever, at ui = si = 0.5, the peak of vertical FAS empirical
activity in Figure 5b is at ki equal to approximately 0.225, which corresponds precisely
to that in Figures 3b and c (at ui = si = 0.5).
Finally, Figure 5c shows the empirical relationship between predicted FASij with si
and ui at ki = 0.5. Consistent with the results above, vertical FAS co-exists with horizontal FAS, but horizontal MNE activity is more prevalent.
6. Conclusions
Finding vertical MNE activity has remained relatively elusive in econometric analyses
of bilateral aggregate FAS data. This paper has offered an approach to try to better
understand empirically and theoretically the relationships between horizontal and
vertical MNEs’ bilateral aggregate foreign affiliate sales (FAS) and countries’ relative
factor endowments. By extending the KC model with only skilled and unskilled
labor to include a third factor (physical capital) and a third country (ROW) as in
Bergstrand and Egger (2007), we could explain theoretically the complex, nonlinear,
nonmonotonic empirical relationships between bilateral FAS flows of two countries
and their relative endowments of skilled labor, unskilled labor, and physical capital.
Our empirical evidence suggests that both horizontal and vertical motivations for
FAS exist in the bilateral aggregate FAS data—and physical capital matters in the
explanation.
Data Appendix
Bilateral foreign affiliate sales data are from UNCTAD (country profiles) for 1986–
2000. GDPs are from the World Bank’s World Development Indicators (2004). We followed Carr et al. (2001) by deflating nominal foreign affiliate sales in US dollars by
host country producer price indices (base year 2000) taken from the World Development Indicators. Physical capital stocks are computed by using the perpetual inventory
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
963
method following Leamer (1984), using gross fixed capital formation and investment
deflator data from the World Development Indicators and assuming a depreciation
rate of 13.3%. Data on human capital endowments were kindly provided by Scott
Baier and are based on information in the World Development Indicators on school
enrollment (see Baier et al., 2006). Remaining workers are classified as unskilled.
Bilateral distance was computed using “great circle” distances. The country trade
resistance and investment resistance indexes are from Carr et al. (2001), kindly provided by Keith Maskus. The exporting (FAS parent) and importing (host) countries
include the following: Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile,
Colombia, Denmark, Egypt (imports/FAS host only), Finland, France, Germany,
Greece, Hong Kong, Ireland, Israel, Italy, Japan, Korea, Mexico, Netherlands, New
Zealand, Norway, Philippines, Portugal, Singapore, South Africa, Spain, Sweden, Switzerland, Turkey, UK, USA, and Venezuela.
References
Alfaro, Laura and Andrew Charlton, “Intra-industry Foreign Direct Investment,” American
Economic Review 99 (2009):2096–119.
Anderson, James E. and Eric van Wincoop, “Gravity with Gravitas: A Solution to the Border
Puzzle,” American Economic Review 93 (2003):170–92.
Baier, Scott L., Gerald P. Dwyer, Jr., and Robert Tamura, “How Important are Capital and
Total Factor Productivity for Economic Growth?” Economic Inquiry 44 (2006):23–49.
Baier, Scott L. and Jeffrey H. Bergstrand, “Do Free Trade Agreements Actually Increase
Members’ International Trade?” Journal of International Economics 71 (2007):72–95.
———, “Bonus Vetus OLS: A Simple Method for Approximating International Trade-cost
Effects using the Gravity Equation,” Journal of International Economics 77 (2009):77–85.
Bergstrand, Jeffrey H. and Peter Egger, “A Knowledge-and-physical-capital Model of International Trade Flows, Foreign Direct Investment, and Multinational Enterprises,” Journal of
International Economics 73 (2007): 278–308.
———, “Gravity Equations and Frictions in the World Economy,” in Daniel Bernhofen, Rod
Falvey, David Greenaway, and Udo Kreickemeier (eds), Palgrave Handbook of International
Trade, New York, NY: Palgrave Macmillan (2011).
Bernard, Andrew B., J. Bradford Jensen, and Peter K. Schott, “Importers, Exporters, and Multinationals: A Portrait of Firms in the U.S. that Trade Goods,” Tuck School of Business at
Dartmouth working paper 2005–17 (2005).
Blonigen, Bruce A., “A Review of the Empirical Literature on FDI Determinants,” Atlantic
Economic Journal 33 (2005):383–403.
Blonigen, Bruce A. and Jeremy Piger, “Determinants of Foreign Direct Investment,” National
Bureau of Economic Research working paper 16704 (2011).
Blonigen, Bruce A., Ronald B. Davies, and Keith Head, “Estimating the Knowledge-capital
Model of the Multinational Enterprise: Comment,” American Economic Review 93
(2003):980–94.
Braconier, Henrik, Pehr-Johan Norbäck, and Dieter Urban, “Reconciling the Evidence on the
Knowledge-capital Model,” Review of International Economics 13 (2005):770–86.
Carr, David, James R. Markusen, and Keith E. Maskus, “Estimating the Knowledge-capital
Model of the Multinational Enterprise,” American Economic Review 91 (2001):693–708.
———, “Estimating the Knowledge-capital Model of the Multinational Enterprise: Reply,”
American Economic Review 93 (2003):995–1001.
Davies, Ronald B., “Hunting High and Low for Vertical FDI,” Review of International Economics 16 (2008):250–67.
Goldin, Claudia and Lawrence Katz, “The Origins of Technology–Skill Complementarity,”
Quarterly Journal of Economics 113 (1998):693–732.
© 2013 John Wiley & Sons Ltd
964
Jeffrey H. Bergstrand and Peter Egger
Griliches, Z., “Capital-Skill Complementarity,” Review of Economics and Statistics 51
(1969):465–68.
Helpman, Elhanan, “Trade, FDI, and the Organization of Firms.” Journal of Economic Literature 46 (2006):589–630.
Helpman, Elhanan, Marc J. Melitz, and Stephen R. Yeaple, “Export Versus FDI with Heterogeneous Firms,” American Economic Review 94 (2004):300–16.
Leamer, Edward E., Sources of International Comparative Advantage: Theory and Evidence,
Cambridge, MA: MIT Press (1984).
Markusen, James R., Multinational Firms and the Theory of International Trade. Cambridge,
MA: MIT Press (2002).
Markusen, James R. and Keith E. Maskus, “Multinational Firms: Reconciling Theory and Evidence,” in Magnus Blomstrom and Linda Goldberg (eds), Topics in Empirical International
Economics: A Festschrift in Honor of Robert E. Lipsey, Chicago: University of Chicago Press
(2001).
———, “Discriminating Among Alternative Theories of the Multinational Enterprise,” Review
of International Economics 10 (2002):694–707.
Santos Silva, J.M.C. and Silvana Tenreyro, “The Log of Gravity,” Review of Economics and Statistics 88 (2006):641–58.
Slaughter, Matthew J., “Production Transfer withing Multinational Enterprises and American
Wages,” Journal of International Economics 50 (2000):449–72.
Notes
1. This is implied by two peaks in the Edgeworth box relating the parent country’s skilled labor
share to FDI/FAS, one for horizontal FDI/FAS flows and one for vertical FDI/FAS flows.
2. Most FDI studies using the gravity equation simply justify using it by analogy to the theoretical foundations for the trade gravity equation. However, see Bergstrand and Egger (2007)
for a theoretical foundation for gravity equations of bilateral FDI and FAS flows, simultaneously with one for trade flows, in the presence of national and multinational firms. See
Bergstrand and Egger (2011) for a survey of the literature.
3. Braconier et al. (2005) find some evidence of vertical FAS. However, their 2 × 2 × 2 approach
has a limitation because there may exist HMNEs in the factor-endowment space where VMNEs
are supposed to be uniquely identified, as discussed in the next section.
4. In fairness, Carr et al. (2003) candidly indicated that finding a “central regression specification” is a very difficult task.
5. We note now that the discussion above has important implications for hypotheses about the
relationship between GDP similarity and FASij. In our three-factor, three-country world, when
ui is at its mean the cell in the middle of the Edgeworth box relating ki and si may not be where
i and j are identically sized in absolute factor endowments (for some given endowments for
ROW), because ui may not be precisely 0.5 (but as noted above, it will be close). Moreover, a
proportionate reduction in ki and si—such that ki/si is unchanged—but holding ui at its mean—
changes i’s and j’s relative economic sizes and also their relative factor endowments. This differs
from the two-factor KC world examined in all the previous studies (also with only two countries) where a movement along the Southwest–Northeast (SW–NE) diagonal implies a change
in relative economic sizes (absolute factor endowments) of the two countries without a change
in relative factor endowments. In our three-factor world, a movement along this diagonal also
changes relative factor endowments.
6. We have done extensive sensitivity analyses for various alternative values of the parameters,
and the results are qualitatively robust and available on request.
7. Note that all figures are indexed between 0 and 100. Hence, the theoretical figures are not
designed to predict effects quantitatively, just qualitatively.
8. Recall that formal theoretical foundations for the gravity equation are based upon
N-country worlds, so the ROW is taken into account.
© 2013 John Wiley & Sons Ltd
SHOULDN’T PHYSICAL CAPITAL ALSO MATTER FOR MNES?
965
9. Regarding other “third-country” effects such as ROW trade and investment barriers, these
effects are more difficult to capture because any country-specific dummies would preclude
cross-section variation in si, ki, and ui, cf. Anderson and van Wincoop (2003) or Baier and
Bergstrand (2009). Moreover, in a panel, such effects would require country and time dummies,
which would also preclude variation in sit,kit, and uit, cf. Baier and Bergstrand (2007). We leave
this issue for researchers to address in the future.
10. Variables si, ki, and ui are not expressed in logs, so their coefficients are not reflecting
“elasticities.”
© 2013 John Wiley & Sons Ltd